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Question
Express the following recurring decimal as a rational number:
`0.bar32`
Solution
`0.bar32` = 0.323232…
= 0.32 + 0.0032 + 0.000032 + …
Here, 0.32, 0.0032, 0.000032, … are in G.P. with a = 0.32 and r = 0.01
Since, | r | = |0.01| < 1
∴ Sum to infinity exists.
∴ Sum to infinity = `"a"/(1 - "r")`
∴ `0.bar32` = `0.32/(1 - (0.01)) = 0.32/0.99`
∴ `0.bar32 = 32/99`.
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